Introduction The social defeat hypothesis (SDH) suggests that a chronic experience of increases the likelihood development psychosis. SDH indicates negative exclusion leads to an increase in baseline activity mesolimbic dopamine system (MDS), which turn onset Social models have previously been produced using animal and preclinical literature; however, these theories not fully tested human clini...

Neural Ordinary Differential Equations (NODE) have emerged as a novel approach to deep learning, where instead of specifying discrete sequence hidden layers, it parameterizes the derivative state using neural network [1]. The solution underlying dynamical system is flow, and various works explored universality flows, in sense being able approximate any analytical function. In this paper we pres...

Diffusion processes intended to model the continuous state space limit of birth–death processes, chemical reactions, and other discrete particle systems often involve multiplicative noise where the diffusion vanishes near one (or more) of the state space boundaries. Standard direct numerical simulation schemes for the associated stochastic differential equations run the risk of “overshooting”, ...

In this paper, on the space of smooth sections of a SL(2, R)-homogeneous vector bundle. over the upper half plane we study the SL(2, R) structure for the eigenspaces of the Cru;;imir operator. That is, we determine its Jordan-Holder' sequence and the sode filttation. We compute a suitable generalized principal series having as a quotient a giver} eigenspace. We also give an integral equation wh...

In this paper we consider an alternative approach to “un-reduction”. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have call...

Cartesian Genetic Programming (CGP) is applied to solving differential equations (DE). We illustrate that repeated elements in analytic solutions to DE can be exploited under GP. An analysis is carried out of the search space in tree and CGP frameworks, examining the complexity of different DE problems. Experimental results are provided against benchmark ordinary and partial differential equati...

We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan–Kähler theorem. We consider a linear partial differential operator P given by the two Helmholtz conditions expressed in terms of semi-basic 1-forms and study its formal integrability. We prove that P is involutive and there is only one obst...

-This paper deals with the adapted Milstein method for solving linear stochastic delay differential equations. It is proved that the numerical method is mean-square (MS) stable under suitable conditions. The obtained result shows that the method preserves the stability property of a class of linear constant-coefficient problems. This is also verified by several numerical examples. (~) 2006 Else...